Is it normal to receive a lot of "eye contact" from a woman who's been in a long term relationship with a guy?

So why not just ask her? Obviously, she's into you and you're into her, too. Just open up a conversation about it and see where it goes. Take my advice - from experience - and don't open up an intimate relationship with her as long as she's with someone else. I did that once and got so burned because she was afraid of having to come out. I got dumpered for the boy. So be careful - but really - sounds like it might be worth exploring! Good luck!